Calculus Examples

$y - 3 = \frac{1}{96} \cdot (x - 16)$

Step 1

Simplify $\frac{1}{96} \cdot (x - 16)$ .

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Step 1.1

Rewrite.

$y - 3 = 0 + 0 + \frac{1}{96} \cdot (x - 16)$

Step 1.2

Simplify by adding zeros.

$y - 3 = \frac{1}{96} \cdot (x - 16)$

Step 1.3

Apply the distributive property.

$y - 3 = \frac{1}{96} x + \frac{1}{96} \cdot - 16$

Step 1.4

Combine $\frac{1}{96}$ and $x$ .

$y - 3 = \frac{x}{96} + \frac{1}{96} \cdot - 16$

Step 1.5

Cancel the common factor of $16$ .

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Step 1.5.1

Factor $16$ out of $96$ .

$y - 3 = \frac{x}{96} + \frac{1}{16 (6)} \cdot - 16$

Step 1.5.2

Factor $16$ out of $- 16$ .

$y - 3 = \frac{x}{96} + \frac{1}{16 \cdot 6} \cdot (16 \cdot - 1)$

Step 1.5.3

Cancel the common factor.

$y - 3 = \frac{x}{96} + \frac{1}{16 \cdot 6} \cdot (16 \cdot - 1)$

Step 1.5.4

Rewrite the expression.

$y - 3 = \frac{x}{96} + \frac{1}{6} \cdot - 1$

Step 1.6

Combine $\frac{1}{6}$ and $- 1$ .

$y - 3 = \frac{x}{96} + \frac{- 1}{6}$

Step 1.7

Move the negative in front of the fraction.

$y - 3 = \frac{x}{96} - \frac{1}{6}$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Add $3$ to both sides of the equation.

$y = \frac{x}{96} - \frac{1}{6} + 3$

Step 2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = \frac{x}{96} - \frac{1}{6} + 3 \cdot \frac{6}{6}$

Step 2.3

Combine $3$ and $\frac{6}{6}$ .

$y = \frac{x}{96} - \frac{1}{6} + \frac{3 \cdot 6}{6}$

Step 2.4

Combine the numerators over the common denominator.

$y = \frac{x}{96} + \frac{- 1 + 3 \cdot 6}{6}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3$ by $6$ .

$y = \frac{x}{96} + \frac{- 1 + 18}{6}$

Step 2.5.2

Add $- 1$ and $18$ .

$y = \frac{x}{96} + \frac{17}{6}$